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Volume 30, Issue 5
A Neural Network Approach to Sampling Based Learning Control for Quantum System with Uncertainty

Jingshi Li, Song Chen, Yanzhao Cao & Zhao Sun

DOI: 10.4208/cicp.OA-2020-0182

Commun. Comput. Phys., 30 (2021), pp. 1453-1473.

Published online: 2021-10

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  • Abstract

Robust control design for quantum systems with uncertainty is a key task for developing practical quantum technology. In this paper, we apply neural networks to learn the control of a quantum system with uncertainty. By exploiting the auto differentiation function developed for neural network models, our method avoids the manual computation of the gradient of the cost function as required in traditional methods. We implement our method using two algorithms. One uses neural networks to learn both the states and the controls and one uses neural networks to learn only the controls but solve the states by finite difference methods. Both algorithms incorporate the sampling-based learning process into the training of the networks. The performance of the algorithms is evaluated on a practical numerical example, followed by a detailed discussion about the advantage and trade-offs between our method and the other numerical schemes.

  • Keywords

Optimal control, quantum computing, uncertainty quantification, deep neural network.

  • AMS Subject Headings

49N05, 68Q12, 93E03

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-30-1453, author = {Li , JingshiChen , SongCao , Yanzhao and Sun , Zhao}, title = {A Neural Network Approach to Sampling Based Learning Control for Quantum System with Uncertainty}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {5}, pages = {1453--1473}, abstract = {

Robust control design for quantum systems with uncertainty is a key task for developing practical quantum technology. In this paper, we apply neural networks to learn the control of a quantum system with uncertainty. By exploiting the auto differentiation function developed for neural network models, our method avoids the manual computation of the gradient of the cost function as required in traditional methods. We implement our method using two algorithms. One uses neural networks to learn both the states and the controls and one uses neural networks to learn only the controls but solve the states by finite difference methods. Both algorithms incorporate the sampling-based learning process into the training of the networks. The performance of the algorithms is evaluated on a practical numerical example, followed by a detailed discussion about the advantage and trade-offs between our method and the other numerical schemes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0182}, url = {http://global-sci.org/intro/article_detail/cicp/19936.html} }
TY - JOUR T1 - A Neural Network Approach to Sampling Based Learning Control for Quantum System with Uncertainty AU - Li , Jingshi AU - Chen , Song AU - Cao , Yanzhao AU - Sun , Zhao JO - Communications in Computational Physics VL - 5 SP - 1453 EP - 1473 PY - 2021 DA - 2021/10 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0182 UR - https://global-sci.org/intro/article_detail/cicp/19936.html KW - Optimal control, quantum computing, uncertainty quantification, deep neural network. AB -

Robust control design for quantum systems with uncertainty is a key task for developing practical quantum technology. In this paper, we apply neural networks to learn the control of a quantum system with uncertainty. By exploiting the auto differentiation function developed for neural network models, our method avoids the manual computation of the gradient of the cost function as required in traditional methods. We implement our method using two algorithms. One uses neural networks to learn both the states and the controls and one uses neural networks to learn only the controls but solve the states by finite difference methods. Both algorithms incorporate the sampling-based learning process into the training of the networks. The performance of the algorithms is evaluated on a practical numerical example, followed by a detailed discussion about the advantage and trade-offs between our method and the other numerical schemes.

Li , JingshiChen , SongCao , Yanzhao and Sun , Zhao. (2021). A Neural Network Approach to Sampling Based Learning Control for Quantum System with Uncertainty. Communications in Computational Physics. 30 (5). 1453-1473. doi:10.4208/cicp.OA-2020-0182
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